How to use blender to create a grid cylinder?
One of   procedural ways to create the cylinder and have its topology consisting of even quads is array a plane to create big plane and bend it afterwards.


Add a plane, rotate it so it's oriented up (along Z axis). Put its origin point in the corner (snap 3D cursor to selection when that vertex is selected and in Object mode use Origin To 3D Cursor).
Start adding modifiers, first will be Array. Set it to array along Z axis (if using default Relative Offset set value of 1 to the Z axis in the modifier options). Set number of iterations so that the height of final result is as height of desired cylinder.
Add another Array modifier and set this one to array along horizontal axes (in case of screenshot X). Set number of iterations to number of edges of cylinder.
Add Simple Deform modifier. Set it to Bend mode, then enter value for Angle to 360 degrees.




The modifier stack in this case is



Otherwise you can add a cylinder, enter Edit mode and use Ctrl+R to add loopcuts along its edges. This will be destructive change to geometry.